LMFDB - Embedded newform 308.2.j.c.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 11x^{10} - 18x^{9} + 48x^{8} - 22x^{7} + 80x^{6} + 68x^{5} + 26x^{4} - 24x^{3} + 9x^{2} + 1 $ x^12 - 4x^11 + 11x^10 - 18x^9 + 48x^8 - 22x^7 + 80x^6 + 68x^5 + 26x^4 - 24x^3 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.2
Root			$0.573758 + 1.76585i$ of defining polynomial
Character	$\chi$	$=$	308.141
Dual form			308.2.j.c.225.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06640 - 0.774782i) q^{3} +(-1.02103 - 3.14242i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.390138 + 1.20072i) q^{9} +O(q^{10})$	\(q+(1.06640 - 0.774782i) q^{3} +(-1.02103 - 3.14242i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.390138 + 1.20072i) q^{9} +(1.37215 - 3.01947i) q^{11} +(0.176619 - 0.543577i) q^{13} +(-3.52351 - 2.55998i) q^{15} +(-1.58193 - 4.86868i) q^{17} +(-4.67915 + 3.39960i) q^{19} -1.31814 q^{21} +7.20716 q^{23} +(-4.78720 + 3.47810i) q^{25} +(1.73624 + 5.34359i) q^{27} +(8.32105 + 6.04559i) q^{29} +(3.27397 - 10.0762i) q^{31} +(-0.876173 - 4.28307i) q^{33} +(-1.02103 + 3.14242i) q^{35} +(0.356105 + 0.258725i) q^{37} +(-0.232808 - 0.716509i) q^{39} +(-6.77984 + 4.92584i) q^{41} +1.53780 q^{43} +4.17152 q^{45} +(8.06579 - 5.86014i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-5.45913 - 3.96629i) q^{51} +(-2.98993 + 9.20205i) q^{53} +(-10.8895 - 1.22890i) q^{55} +(-2.35588 + 7.25065i) q^{57} +(1.66051 + 1.20643i) q^{59} +(2.87574 + 8.85062i) q^{61} +(1.02140 - 0.742087i) q^{63} -1.88848 q^{65} -1.05858 q^{67} +(7.68568 - 5.58398i) q^{69} +(-1.77103 - 5.45067i) q^{71} +(6.27607 + 4.55983i) q^{73} +(-2.41028 + 7.41807i) q^{75} +(-2.88489 + 1.63627i) q^{77} +(-0.123928 + 0.381412i) q^{79} +(2.92744 + 2.12691i) q^{81} +(1.72117 + 5.29722i) q^{83} +(-13.6842 + 9.94218i) q^{85} +13.5575 q^{87} +2.15666 q^{89} +(-0.462394 + 0.335949i) q^{91} +(-4.31554 - 13.2819i) q^{93} +(15.4606 + 11.2328i) q^{95} +(-1.13826 + 3.50320i) q^{97} +(3.09022 + 2.82558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.06640	−	0.774782i	0.615684	−	0.447320i	−0.235727	−	0.971819i	$-0.575747\pi$
$3$	1.06640	−	0.774782i	0.615684	−	0.447320i	0.851411	+	0.524499i	$0.175747\pi$
$4$		0			0
$5$	−1.02103	−	3.14242i	−0.456620	−	1.40533i	−0.869222	−	0.494421i	$-0.835380\pi$
$5$	−1.02103	−	3.14242i	−0.456620	−	1.40533i	0.412602	−	0.910911i	$-0.364620\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	−0.390138	+	1.20072i	−0.130046	+	0.400241i
$10$		0			0
$11$	1.37215	−	3.01947i	0.413719	−	0.910404i
$11$	1.37215	−	3.01947i	0.413719	−	0.910404i
$12$		0			0
$13$	0.176619	−	0.543577i	0.0489852	−	0.150761i	−0.923572	−	0.383425i	$-0.874744\pi$
$13$	0.176619	−	0.543577i	0.0489852	−	0.150761i	0.972557	+	0.232664i	$0.0747443\pi$
$14$		0			0
$15$	−3.52351	−	2.55998i	−0.909767	−	0.660985i
$16$		0			0
$17$	−1.58193	−	4.86868i	−0.383675	−	1.18083i	−0.937437	−	0.348154i	$-0.886809\pi$
$17$	−1.58193	−	4.86868i	−0.383675	−	1.18083i	0.553763	−	0.832675i	$-0.313191\pi$
$18$		0			0
$19$	−4.67915	+	3.39960i	−1.07347	+	0.779923i	−0.976533	−	0.215368i	$-0.930905\pi$
$19$	−4.67915	+	3.39960i	−1.07347	+	0.779923i	−0.0969386	+	0.995290i	$0.530905\pi$
$20$		0			0
$21$	−1.31814			−0.287641
$22$		0			0
$23$	7.20716			1.50280			0.751398	−	0.659849i	$-0.229380\pi$
$23$	7.20716			1.50280			0.751398	+	0.659849i	$0.229380\pi$
$24$		0			0
$25$	−4.78720	+	3.47810i	−0.957440	+	0.695621i
$26$		0			0
$27$	1.73624	+	5.34359i	0.334139	+	1.02837i
$28$		0			0
$29$	8.32105	+	6.04559i	1.54518	+	1.12264i	0.946980	+	0.321291i	$0.104117\pi$
$29$	8.32105	+	6.04559i	1.54518	+	1.12264i	0.598199	+	0.801348i	$0.295883\pi$
$30$		0			0
$31$	3.27397	−	10.0762i	0.588022	−	1.80974i	0.00123996	−	0.999999i	$-0.499605\pi$
$31$	3.27397	−	10.0762i	0.588022	−	1.80974i	0.586782	−	0.809745i	$-0.300395\pi$
$32$		0			0
$33$	−0.876173	−	4.28307i	−0.152522	−	0.745586i
$34$		0			0
$35$	−1.02103	+	3.14242i	−0.172586	+	0.531166i
$36$		0			0
$37$	0.356105	+	0.258725i	0.0585433	+	0.0425342i	0.616672	−	0.787220i	$-0.288480\pi$
$37$	0.356105	+	0.258725i	0.0585433	+	0.0425342i	−0.558129	+	0.829754i	$0.688480\pi$
$38$		0			0
$39$	−0.232808	−	0.716509i	−0.0372791	−	0.114733i
$40$		0			0
$41$	−6.77984	+	4.92584i	−1.05883	+	0.769287i	−0.973872	−	0.227097i	$-0.927076\pi$
$41$	−6.77984	+	4.92584i	−1.05883	+	0.769287i	−0.0849607	+	0.996384i	$0.527076\pi$
$42$		0			0
$43$	1.53780			0.234512			0.117256	−	0.993102i	$-0.462590\pi$
$43$	1.53780			0.234512			0.117256	+	0.993102i	$0.462590\pi$
$44$		0			0
$45$	4.17152			0.621853
$46$		0			0
$47$	8.06579	−	5.86014i	1.17652	−	0.854789i	0.184742	−	0.982787i	$-0.440855\pi$
$47$	8.06579	−	5.86014i	1.17652	−	0.854789i	0.991774	+	0.127998i	$0.0408552\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	−5.45913	−	3.96629i	−0.764431	−	0.555392i
$52$		0			0
$53$	−2.98993	+	9.20205i	−0.410698	+	1.26400i	0.505344	+	0.862918i	$0.331366\pi$
$53$	−2.98993	+	9.20205i	−0.410698	+	1.26400i	−0.916042	+	0.401081i	$0.868634\pi$
$54$		0			0
$55$	−10.8895	−	1.22890i	−1.46833	−	0.165704i
$56$		0			0
$57$	−2.35588	+	7.25065i	−0.312044	+	0.960372i
$58$		0			0
$59$	1.66051	+	1.20643i	0.216180	+	0.157064i	0.690606	−	0.723232i	$-0.257344\pi$
$59$	1.66051	+	1.20643i	0.216180	+	0.157064i	−0.474425	+	0.880296i	$0.657344\pi$
$60$		0			0
$61$	2.87574	+	8.85062i	0.368201	+	1.13321i	0.947952	+	0.318412i	$0.103150\pi$
$61$	2.87574	+	8.85062i	0.368201	+	1.13321i	−0.579752	+	0.814793i	$0.696850\pi$
$62$		0			0
$63$	1.02140	−	0.742087i	0.128684	−	0.0934942i
$64$		0			0
$65$	−1.88848			−0.234237
$66$		0			0
$67$	−1.05858			−0.129326			−0.0646630	−	0.997907i	$-0.520597\pi$
$67$	−1.05858			−0.129326			−0.0646630	+	0.997907i	$0.520597\pi$
$68$		0			0
$69$	7.68568	−	5.58398i	0.925248	−	0.672232i
$70$		0			0
$71$	−1.77103	−	5.45067i	−0.210183	−	0.646876i	−0.999461	−	0.0328395i	$-0.989545\pi$
$71$	−1.77103	−	5.45067i	−0.210183	−	0.646876i	0.789278	−	0.614036i	$-0.210455\pi$
$72$		0			0
$73$	6.27607	+	4.55983i	0.734558	+	0.533688i	0.891002	−	0.453999i	$-0.150003\pi$
$73$	6.27607	+	4.55983i	0.734558	+	0.533688i	−0.156444	+	0.987687i	$0.550003\pi$
$74$		0			0
$75$	−2.41028	+	7.41807i	−0.278315	+	0.856565i
$76$		0			0
$77$	−2.88489	+	1.63627i	−0.328764	+	0.186470i
$78$		0			0
$79$	−0.123928	+	0.381412i	−0.0139430	+	0.0429122i	−0.957786	−	0.287482i	$-0.907182\pi$
$79$	−0.123928	+	0.381412i	−0.0139430	+	0.0429122i	0.943843	+	0.330394i	$0.107182\pi$
$80$		0			0
$81$	2.92744	+	2.12691i	0.325271	+	0.236323i
$82$		0			0
$83$	1.72117	+	5.29722i	0.188923	+	0.581445i	0.999994	−	0.00350257i	$-0.00111491\pi$
$83$	1.72117	+	5.29722i	0.188923	+	0.581445i	−0.811071	+	0.584948i	$0.801115\pi$
$84$		0			0
$85$	−13.6842	+	9.94218i	−1.48426	+	1.07838i
$86$		0			0
$87$	13.5575			1.45352
$88$		0			0
$89$	2.15666			0.228605			0.114303	−	0.993446i	$-0.463537\pi$
$89$	2.15666			0.228605			0.114303	+	0.993446i	$0.463537\pi$
$90$		0			0
$91$	−0.462394	+	0.335949i	−0.0484721	+	0.0352170i
$92$		0			0
$93$	−4.31554	−	13.2819i	−0.447500	−	1.37726i
$94$		0			0
$95$	15.4606	+	11.2328i	1.58622	+	1.15246i
$96$		0			0
$97$	−1.13826	+	3.50320i	−0.115573	+	0.355696i	−0.992066	−	0.125718i	$-0.959877\pi$
$97$	−1.13826	+	3.50320i	−0.115573	+	0.355696i	0.876493	+	0.481414i	$0.159877\pi$
$98$		0			0
$99$	3.09022	+	2.82558i	0.310578	+	0.283982i
$100$		0			0
$101$	−0.176726	+	0.543907i	−0.0175849	+	0.0541208i	−0.959464	−	0.281831i	$-0.909058\pi$
$101$	−0.176726	+	0.543907i	−0.0175849	+	0.0541208i	0.941879	+	0.335952i	$0.109058\pi$
$102$		0			0
$103$	−2.67572	−	1.94402i	−0.263647	−	0.191550i	0.448107	−	0.893980i	$-0.352099\pi$
$103$	−2.67572	−	1.94402i	−0.263647	−	0.191550i	−0.711753	+	0.702430i	$0.752099\pi$
$104$		0			0
$105$	1.34586	+	4.14214i	0.131343	+	0.404231i
$106$		0			0
$107$	7.08185	−	5.14527i	0.684629	−	0.497412i	−0.190261	−	0.981733i	$-0.560934\pi$
$107$	7.08185	−	5.14527i	0.684629	−	0.497412i	0.874890	+	0.484322i	$0.160934\pi$
$108$		0			0
$109$	−16.8958			−1.61832			−0.809161	−	0.587587i	$-0.800078\pi$
$109$	−16.8958			−1.61832			−0.809161	+	0.587587i	$0.800078\pi$
$110$		0			0
$111$	0.580204			0.0550706
$112$		0			0
$113$	−11.6277	+	8.44803i	−1.09384	+	0.794723i	−0.980044	−	0.198780i	$-0.936302\pi$
$113$	−11.6277	+	8.44803i	−1.09384	+	0.794723i	−0.113799	+	0.993504i	$0.536302\pi$
$114$		0			0
$115$	−7.35875	−	22.6479i	−0.686207	−	2.11193i
$116$		0			0
$117$	0.583779	+	0.424140i	0.0539704	+	0.0392118i
$118$		0			0
$119$	−1.58193	+	4.86868i	−0.145015	+	0.446311i
$120$		0			0
$121$	−7.23440	−	8.28634i	−0.657672	−	0.753304i
$122$		0			0
$123$	−3.41354	+	10.5058i	−0.307788	+	0.947275i
$124$		0			0
$125$	2.45205	+	1.78152i	0.219318	+	0.159344i
$126$		0			0
$127$	−0.985124	−	3.03190i	−0.0874156	−	0.269038i	0.897787	−	0.440429i	$-0.145174\pi$
$127$	−0.985124	−	3.03190i	−0.0874156	−	0.269038i	−0.985203	+	0.171391i	$0.945174\pi$
$128$		0			0
$129$	1.63990	−	1.19146i	0.144385	−	0.104902i
$130$		0			0
$131$	4.48314			0.391694			0.195847	−	0.980634i	$-0.437254\pi$
$131$	4.48314			0.391694			0.195847	+	0.980634i	$0.437254\pi$
$132$		0			0
$133$	5.78375			0.501515
$134$		0			0
$135$	15.0190	−	10.9120i	1.29263	−	0.939152i
$136$		0			0
$137$	−3.53475	−	10.8788i	−0.301994	−	0.929442i	−0.980782	−	0.195107i	$-0.937494\pi$
$137$	−3.53475	−	10.8788i	−0.301994	−	0.929442i	0.678788	−	0.734334i	$-0.262506\pi$
$138$		0			0
$139$	−5.82887	−	4.23492i	−0.494398	−	0.359202i	0.312475	−	0.949926i	$-0.398842\pi$
$139$	−5.82887	−	4.23492i	−0.494398	−	0.359202i	−0.806873	+	0.590725i	$0.798842\pi$
$140$		0			0
$141$	4.06099	−	12.4984i	0.341997	−	1.05256i
$142$		0			0
$143$	−1.39897	−	1.27916i	−0.116987	−	0.106969i
$144$		0			0
$145$	10.5017	−	32.3210i	0.872120	−	2.68411i
$146$		0			0
$147$	1.06640	+	0.774782i	0.0879548	+	0.0639029i
$148$		0			0
$149$	0.440435	+	1.35552i	0.0360818	+	0.111048i	0.967475	−	0.252966i	$-0.0814060\pi$
$149$	0.440435	+	1.35552i	0.0360818	+	0.111048i	−0.931393	+	0.364014i	$0.881406\pi$
$150$		0			0
$151$	−0.837621	+	0.608567i	−0.0681646	+	0.0495245i	−0.621346	−	0.783537i	$-0.713414\pi$
$151$	−0.837621	+	0.608567i	−0.0681646	+	0.0495245i	0.553181	+	0.833061i	$0.313414\pi$
$152$		0			0
$153$	6.46311			0.522511
$154$		0			0
$155$	−35.0066			−2.81179
$156$		0			0
$157$	8.25468	−	5.99738i	0.658795	−	0.478643i	−0.207461	−	0.978243i	$-0.566520\pi$
$157$	8.25468	−	5.99738i	0.658795	−	0.478643i	0.866256	+	0.499601i	$0.166520\pi$
$158$		0			0
$159$	3.94114	+	12.1296i	0.312552	+	0.961938i
$160$		0			0
$161$	−5.83072	−	4.23626i	−0.459525	−	0.333864i
$162$		0			0
$163$	−3.57982	+	11.0176i	−0.280393	+	0.862962i	0.707348	+	0.706865i	$0.249891\pi$
$163$	−3.57982	+	11.0176i	−0.280393	+	0.862962i	−0.987742	+	0.156097i	$0.950109\pi$
$164$		0			0
$165$	−12.5646	+	7.12646i	−0.978152	+	0.554794i
$166$		0			0
$167$	1.13007	−	3.47799i	0.0874472	−	0.269135i	−0.897765	−	0.440475i	$-0.854810\pi$
$167$	1.13007	−	3.47799i	0.0874472	−	0.269135i	0.985212	+	0.171341i	$0.0548099\pi$
$168$		0			0
$169$	10.2529	+	7.44920i	0.788688	+	0.573015i
$170$		0			0
$171$	−2.25646	−	6.94468i	−0.172556	−	0.531073i
$172$		0			0
$173$	10.0563	−	7.30634i	0.764567	−	0.555491i	−0.135740	−	0.990744i	$-0.543341\pi$
$173$	10.0563	−	7.30634i	0.764567	−	0.555491i	0.900308	+	0.435254i	$0.143341\pi$
$174$		0			0
$175$	5.91731			0.447306
$176$		0			0
$177$	2.70549			0.203357
$178$		0			0
$179$	19.4438	−	14.1267i	1.45330	−	1.05588i	0.468251	−	0.883596i	$-0.344884\pi$
$179$	19.4438	−	14.1267i	1.45330	−	1.05588i	0.985047	−	0.172287i	$-0.0551156\pi$
$180$		0			0
$181$	−5.14011	−	15.8196i	−0.382061	−	1.17586i	−0.938590	−	0.345035i	$-0.887867\pi$
$181$	−5.14011	−	15.8196i	−0.382061	−	1.17586i	0.556528	−	0.830829i	$-0.312133\pi$
$182$		0			0
$183$	9.92397	+	7.21019i	0.733601	+	0.532992i
$184$		0			0
$185$	0.449428	−	1.38320i	0.0330426	−	0.101695i
$186$		0			0
$187$	−16.8715	−	1.90398i	−1.23377	−	0.139233i
$188$		0			0
$189$	1.73624	−	5.34359i	0.126293	−	0.388689i
$190$		0			0
$191$	−4.44562	−	3.22993i	−0.321674	−	0.233710i	0.415216	−	0.909723i	$-0.363706\pi$
$191$	−4.44562	−	3.22993i	−0.321674	−	0.233710i	−0.736889	+	0.676013i	$0.763706\pi$
$192$		0			0
$193$	−2.38281	−	7.33352i	−0.171518	−	0.527879i	0.827939	−	0.560818i	$-0.189513\pi$
$193$	−2.38281	−	7.33352i	−0.171518	−	0.527879i	−0.999457	+	0.0329393i	$0.989513\pi$
$194$		0			0
$195$	−2.01387	+	1.46316i	−0.144216	+	0.104779i
$196$		0			0
$197$	20.6814			1.47349			0.736743	−	0.676173i	$-0.236363\pi$
$197$	20.6814			1.47349			0.736743	+	0.676173i	$0.236363\pi$
$198$		0			0
$199$	−5.24890			−0.372085			−0.186042	−	0.982542i	$-0.559566\pi$
$199$	−5.24890			−0.372085			−0.186042	+	0.982542i	$0.559566\pi$
$200$		0			0
$201$	−1.12886	+	0.820168i	−0.0796239	+	0.0578502i
$202$		0			0
$203$	−3.17836	−	9.78198i	−0.223077	−	0.686560i
$204$		0			0
$205$	22.4015	+	16.2756i	1.56459	+	1.13674i
$206$		0			0
$207$	−2.81179	+	8.65380i	−0.195433	+	0.601481i
$208$		0			0
$209$	3.84449	+	18.7933i	0.265929	+	1.29996i
$210$		0			0
$211$	−7.58249	+	23.3365i	−0.522000	+	1.60655i	0.248172	+	0.968716i	$0.420170\pi$
$211$	−7.58249	+	23.3365i	−0.522000	+	1.60655i	−0.770172	+	0.637836i	$0.779830\pi$
$212$		0			0
$213$	−6.11170	−	4.44041i	−0.418767	−	0.304252i
$214$		0			0
$215$	−1.57014	−	4.83241i	−0.107083	−	0.329567i
$216$		0			0
$217$	−8.57135	+	6.22745i	−0.581861	+	0.422747i
$218$		0			0
$219$	10.2256			0.690985
$220$		0			0
$221$	−2.92590			−0.196817
$222$		0			0
$223$	−3.35873	+	2.44026i	−0.224918	+	0.163412i	−0.694537	−	0.719457i	$-0.744391\pi$
$223$	−3.35873	+	2.44026i	−0.224918	+	0.163412i	0.469620	+	0.882869i	$0.344391\pi$
$224$		0			0
$225$	−2.30857	−	7.10504i	−0.153904	−	0.473669i
$226$		0			0
$227$	3.01688	+	2.19189i	0.200237	+	0.145481i	0.683386	−	0.730058i	$-0.260507\pi$
$227$	3.01688	+	2.19189i	0.200237	+	0.145481i	−0.483148	+	0.875539i	$0.660507\pi$
$228$		0			0
$229$	−3.46570	+	10.6663i	−0.229020	+	0.704850i	0.768839	+	0.639442i	$0.220835\pi$
$229$	−3.46570	+	10.6663i	−0.229020	+	0.704850i	−0.997859	+	0.0654076i	$0.979165\pi$
$230$		0			0
$231$	−1.80869	+	3.98008i	−0.119003	+	0.261870i
$232$		0			0
$233$	0.0506876	−	0.156000i	0.00332065	−	0.0102199i	−0.949382	−	0.314122i	$-0.898290\pi$
$233$	0.0506876	−	0.156000i	0.00332065	−	0.0102199i	0.952703	+	0.303903i	$0.0982897\pi$
$234$		0			0
$235$	−26.6504	−	19.3627i	−1.73848	−	1.26308i
$236$		0			0
$237$	0.163354	+	0.502753i	0.0106110	+	0.0326573i
$238$		0			0
$239$	−10.0399	+	7.29443i	−0.649429	+	0.471837i	−0.863076	−	0.505073i	$-0.831465\pi$
$239$	−10.0399	+	7.29443i	−0.649429	+	0.471837i	0.213648	+	0.976911i	$0.431465\pi$
$240$		0			0
$241$	−19.9846			−1.28732			−0.643661	−	0.765311i	$-0.722585\pi$
$241$	−19.9846			−1.28732			−0.643661	+	0.765311i	$0.722585\pi$
$242$		0			0
$243$	−12.0860			−0.775319
$244$		0			0
$245$	2.67310	−	1.94212i	0.170778	−	0.124078i
$246$		0			0
$247$	1.02152	+	3.14391i	0.0649977	+	0.200042i
$248$		0			0
$249$	5.93964	+	4.31540i	0.376409	+	0.273477i
$250$		0			0
$251$	−3.54024	+	10.8957i	−0.223458	+	0.687732i	0.774987	+	0.631977i	$0.217756\pi$
$251$	−3.54024	+	10.8957i	−0.223458	+	0.687732i	−0.998444	+	0.0557548i	$0.982244\pi$
$252$		0			0
$253$	9.88932	−	21.7618i	0.621736	−	1.36815i
$254$		0			0
$255$	−6.88979	+	21.2046i	−0.431455	+	1.32788i
$256$		0			0
$257$	5.23610	+	3.80425i	0.326619	+	0.237302i	0.738995	−	0.673711i	$-0.235301\pi$
$257$	5.23610	+	3.80425i	0.326619	+	0.237302i	−0.412376	+	0.911014i	$0.635301\pi$
$258$		0			0
$259$	−0.136020	−	0.418626i	−0.00845187	−	0.0260122i
$260$		0			0
$261$	−10.5054	+	7.63265i	−0.650270	+	0.472449i
$262$		0			0
$263$	5.98706			0.369178			0.184589	−	0.982816i	$-0.440905\pi$
$263$	5.98706			0.369178			0.184589	+	0.982816i	$0.440905\pi$
$264$		0			0
$265$	31.9695			1.96387
$266$		0			0
$267$	2.29985	−	1.67094i	0.140748	−	0.102260i
$268$		0			0
$269$	−0.799707	−	2.46125i	−0.0487590	−	0.150065i	0.923713	−	0.383086i	$-0.125139\pi$
$269$	−0.799707	−	2.46125i	−0.0487590	−	0.150065i	−0.972472	+	0.233021i	$0.925139\pi$
$270$		0			0
$271$	−7.82943	−	5.68842i	−0.475604	−	0.345547i	0.324017	−	0.946051i	$-0.394966\pi$
$271$	−7.82943	−	5.68842i	−0.475604	−	0.345547i	−0.799621	+	0.600505i	$0.794966\pi$
$272$		0			0
$273$	−0.232808	+	0.716509i	−0.0140902	+	0.0433651i
$274$		0			0
$275$	3.93326	+	19.2273i	0.237185	+	1.15945i
$276$		0			0
$277$	−9.14521	+	28.1460i	−0.549482	+	1.69113i	0.160605	+	0.987019i	$0.448655\pi$
$277$	−9.14521	+	28.1460i	−0.549482	+	1.69113i	−0.710087	+	0.704114i	$0.751345\pi$
$278$		0			0
$279$	10.8215	+	7.86225i	0.647864	+	0.470700i
$280$		0			0
$281$	−5.03043	−	15.4821i	−0.300090	−	0.923583i	−0.981464	−	0.191647i	$-0.938617\pi$
$281$	−5.03043	−	15.4821i	−0.300090	−	0.923583i	0.681374	−	0.731936i	$-0.261383\pi$
$282$		0			0
$283$	−9.25065	+	6.72099i	−0.549894	+	0.399522i	−0.827746	−	0.561102i	$-0.810377\pi$
$283$	−9.25065	+	6.72099i	−0.549894	+	0.399522i	0.277852	+	0.960624i	$0.410377\pi$
$284$		0			0
$285$	25.1900			1.49213
$286$		0			0
$287$	8.38034			0.494676
$288$		0			0
$289$	−7.44827	+	5.41149i	−0.438134	+	0.318323i
$290$		0			0
$291$	1.50038	+	4.61770i	0.0879539	+	0.270694i
$292$		0			0
$293$	−11.1674	−	8.11363i	−0.652409	−	0.474003i	0.211682	−	0.977339i	$-0.432106\pi$
$293$	−11.1674	−	8.11363i	−0.652409	−	0.474003i	−0.864091	+	0.503336i	$0.832106\pi$
$294$		0			0
$295$	2.09568	−	6.44984i	0.122015	−	0.375524i
$296$		0			0
$297$	18.5172	+	2.08970i	1.07448	+	0.121257i
$298$		0			0
$299$	1.27292	−	3.91764i	0.0736149	−	0.226563i
$300$		0			0
$301$	−1.24410	−	0.903895i	−0.0717090	−	0.0520997i
$302$		0			0
$303$	0.232949	+	0.716945i	0.0133826	+	0.0411874i
$304$		0			0
$305$	24.8761	−	18.0736i	1.42440	−	1.03489i
$306$		0			0
$307$	−0.591648			−0.0337672			−0.0168836	−	0.999857i	$-0.505374\pi$
$307$	−0.591648			−0.0337672			−0.0168836	+	0.999857i	$0.505374\pi$
$308$		0			0
$309$	−4.35957			−0.248007
$310$		0			0
$311$	8.80050	−	6.39394i	0.499031	−	0.362567i	−0.309616	−	0.950862i	$-0.600200\pi$
$311$	8.80050	−	6.39394i	0.499031	−	0.362567i	0.808647	+	0.588295i	$0.200200\pi$
$312$		0			0
$313$	9.54542	+	29.3778i	0.539539	+	1.66053i	0.733632	+	0.679547i	$0.237824\pi$
$313$	9.54542	+	29.3778i	0.539539	+	1.66053i	−0.194093	+	0.980983i	$0.562176\pi$
$314$		0			0
$315$	−3.37483	−	2.45196i	−0.190150	−	0.138152i
$316$		0			0
$317$	−4.44482	+	13.6798i	−0.249646	+	0.768332i	0.745191	+	0.666851i	$0.232358\pi$
$317$	−4.44482	+	13.6798i	−0.249646	+	0.768332i	−0.994837	+	0.101481i	$0.967642\pi$
$318$		0			0
$319$	29.6722	−	16.8297i	1.66133	−	0.942281i
$320$		0			0
$321$	3.56560	−	10.9738i	0.199012	−	0.612497i
$322$		0			0
$323$	23.9537	+	17.4034i	1.33282	+	0.968350i
$324$		0			0
$325$	1.04511	+	3.21651i	0.0579721	+	0.178420i
$326$		0			0
$327$	−18.0176	+	13.0905i	−0.996374	+	0.723908i
$328$		0			0
$329$	−9.96986			−0.549656
$330$		0			0
$331$	8.89376			0.488845			0.244423	−	0.969669i	$-0.421402\pi$
$331$	8.89376			0.488845			0.244423	+	0.969669i	$0.421402\pi$
$332$		0			0
$333$	−0.449588	+	0.326644i	−0.0246372	+	0.0179000i
$334$		0			0
$335$	1.08085	+	3.32650i	0.0590529	+	0.181746i
$336$		0			0
$337$	7.18685	+	5.22155i	0.391493	+	0.284436i	0.766067	−	0.642761i	$-0.222211\pi$
$337$	7.18685	+	5.22155i	0.391493	+	0.284436i	−0.374574	+	0.927197i	$0.622211\pi$
$338$		0			0
$339$	−5.85436	+	18.0179i	−0.317965	+	0.978597i
$340$		0			0
$341$	−25.9325	−	23.7118i	−1.40432	−	1.28406i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	−25.3945	−	18.4502i	−1.36720	−	0.993326i
$346$		0			0
$347$	8.19305	+	25.2156i	0.439826	+	1.35365i	0.888059	+	0.459729i	$0.152053\pi$
$347$	8.19305	+	25.2156i	0.439826	+	1.35365i	−0.448233	+	0.893917i	$0.647947\pi$
$348$		0			0
$349$	−20.2684	+	14.7259i	−1.08494	+	0.788257i	−0.978538	−	0.206066i	$-0.933934\pi$
$349$	−20.2684	+	14.7259i	−1.08494	+	0.788257i	−0.106405	+	0.994323i	$0.533934\pi$
$350$		0			0
$351$	3.21130			0.171407
$352$		0			0
$353$	−3.64502			−0.194005			−0.0970024	−	0.995284i	$-0.530925\pi$
$353$	−3.64502			−0.194005			−0.0970024	+	0.995284i	$0.530925\pi$
$354$		0			0
$355$	−15.3200	+	11.1306i	−0.813102	+	0.590753i
$356$		0			0
$357$	2.08520	+	6.41759i	0.110361	+	0.339655i
$358$		0			0
$359$	−28.4953	−	20.7031i	−1.50392	−	1.09267i	−0.968785	−	0.247902i	$-0.920259\pi$
$359$	−28.4953	−	20.7031i	−1.50392	−	1.09267i	−0.535140	−	0.844764i	$-0.679741\pi$
$360$		0			0
$361$	4.46585	−	13.7445i	0.235045	−	0.723393i
$362$		0			0
$363$	−14.1348	−	3.23144i	−0.741886	−	0.169607i
$364$		0			0
$365$	7.92082	−	24.3778i	0.414594	−	1.27599i
$366$		0			0
$367$	25.3333	+	18.4057i	1.32239	+	0.960772i	0.999899	+	0.0141984i	$0.00451965\pi$
$367$	25.3333	+	18.4057i	1.32239	+	0.960772i	0.322489	+	0.946573i	$0.395480\pi$
$368$		0			0
$369$	−3.26949	−	10.0625i	−0.170203	−	0.523831i
$370$		0			0
$371$	7.82774	−	5.68718i	0.406396	−	0.295264i
$372$		0			0
$373$	−23.5551			−1.21964			−0.609818	−	0.792542i	$-0.708757\pi$
$373$	−23.5551			−1.21964			−0.609818	+	0.792542i	$0.708757\pi$
$374$		0			0
$375$	3.99514			0.206308
$376$		0			0
$377$	4.75590	−	3.45536i	0.244941	−	0.177960i
$378$		0			0
$379$	2.53400	+	7.79884i	0.130163	+	0.400599i	0.994806	−	0.101786i	$-0.0324558\pi$
$379$	2.53400	+	7.79884i	0.130163	+	0.400599i	−0.864644	+	0.502386i	$0.832456\pi$
$380$		0			0
$381$	−3.39959	−	2.46995i	−0.174166	−	0.126539i
$382$		0			0
$383$	−9.73344	+	29.9565i	−0.497356	+	1.53070i	0.315897	+	0.948793i	$0.397694\pi$
$383$	−9.73344	+	29.9565i	−0.497356	+	1.53070i	−0.813253	+	0.581910i	$0.802306\pi$
$384$		0			0
$385$	8.08742	+	7.39486i	0.412173	+	0.376877i
$386$		0			0
$387$	−0.599954	+	1.84647i	−0.0304974	+	0.0938613i
$388$		0			0
$389$	−15.8772	−	11.5355i	−0.805006	−	0.584871i	0.107372	−	0.994219i	$-0.465756\pi$
$389$	−15.8772	−	11.5355i	−0.805006	−	0.584871i	−0.912378	+	0.409348i	$0.865756\pi$
$390$		0			0
$391$	−11.4012	−	35.0894i	−0.576585	−	1.77455i
$392$		0			0
$393$	4.78080	−	3.47345i	0.241159	−	0.175213i
$394$		0			0
$395$	1.32509			0.0666725
$396$		0			0
$397$	13.0252			0.653715			0.326857	−	0.945074i	$-0.394010\pi$
$397$	13.0252			0.653715			0.326857	+	0.945074i	$0.394010\pi$
$398$		0			0
$399$	6.16777	−	4.48115i	0.308775	−	0.224338i
$400$		0			0
$401$	−0.00736064	−	0.0226537i	−0.000367573	−	0.00113127i	0.950873	−	0.309583i	$-0.100189\pi$
$401$	−0.00736064	−	0.0226537i	−0.000367573	−	0.00113127i	−0.951240	+	0.308451i	$0.900189\pi$
$402$		0			0
$403$	−4.89896	−	3.55930i	−0.244035	−	0.177301i
$404$		0			0
$405$	3.69463	−	11.3709i	0.183588	−	0.565024i
$406$		0			0
$407$	1.26984	−	0.720238i	0.0629438	−	0.0357009i
$408$		0			0
$409$	−7.82027	+	24.0683i	−0.386687	+	1.19010i	0.548562	+	0.836110i	$0.315176\pi$
$409$	−7.82027	+	24.0683i	−0.386687	+	1.19010i	−0.935249	+	0.353991i	$0.884824\pi$
$410$		0			0
$411$	−12.1982	−	8.86248i	−0.601691	−	0.437154i
$412$		0			0
$413$	−0.634260	−	1.95205i	−0.0312099	−	0.0960541i
$414$		0			0
$415$	14.8887	−	10.8173i	0.730858	−	0.530999i
$416$		0			0
$417$	−9.49702			−0.465071
$418$		0			0
$419$	−23.9130			−1.16823			−0.584113	−	0.811672i	$-0.698558\pi$
$419$	−23.9130			−1.16823			−0.584113	+	0.811672i	$0.698558\pi$
$420$		0			0
$421$	23.3377	−	16.9558i	1.13741	−	0.826377i	0.150654	−	0.988587i	$-0.451862\pi$
$421$	23.3377	−	16.9558i	1.13741	−	0.826377i	0.986756	+	0.162209i	$0.0518620\pi$
$422$		0			0
$423$	3.88962	+	11.9710i	0.189120	+	0.582052i
$424$		0			0
$425$	24.5068	+	17.8052i	1.18875	+	0.863681i
$426$		0			0
$427$	2.87574	−	8.85062i	0.139167	−	0.428311i
$428$		0			0
$429$	−2.48292	−	0.280203i	−0.119877	−	0.0135283i
$430$		0			0
$431$	4.52730	−	13.9336i	0.218072	−	0.671158i	−0.780849	−	0.624720i	$-0.785213\pi$
$431$	4.52730	−	13.9336i	0.218072	−	0.671158i	0.998921	−	0.0464377i	$-0.0147869\pi$
$432$		0			0
$433$	−7.87720	−	5.72312i	−0.378554	−	0.275036i	0.382195	−	0.924082i	$-0.375168\pi$
$433$	−7.87720	−	5.72312i	−0.378554	−	0.275036i	−0.760749	+	0.649046i	$0.775168\pi$
$434$		0			0
$435$	−13.8427	−	42.6035i	−0.663707	−	2.04268i
$436$		0			0
$437$	−33.7234	+	24.5015i	−1.61321	+	1.17207i
$438$		0			0
$439$	19.5831			0.934652			0.467326	−	0.884085i	$-0.345217\pi$
$439$	19.5831			0.934652			0.467326	+	0.884085i	$0.345217\pi$
$440$		0			0
$441$	−1.26251			−0.0601197
$442$		0			0
$443$	3.48959	−	2.53534i	0.165795	−	0.120457i	−0.501794	−	0.864987i	$-0.667326\pi$
$443$	3.48959	−	2.53534i	0.165795	−	0.120457i	0.667589	+	0.744530i	$0.267326\pi$
$444$		0			0
$445$	−2.20202	−	6.77712i	−0.104386	−	0.321266i
$446$		0			0
$447$	1.51991	+	1.10428i	0.0718892	+	0.0522306i
$448$		0			0
$449$	9.57930	−	29.4821i	0.452075	−	1.39134i	−0.422460	−	0.906382i	$-0.638833\pi$
$449$	9.57930	−	29.4821i	0.452075	−	1.39134i	0.874535	−	0.484963i	$-0.161167\pi$
$450$		0			0
$451$	5.57046	+	27.2305i	0.262303	+	1.28224i
$452$		0			0
$453$	−0.421728	+	1.29795i	−0.0198145	+	0.0609828i
$454$		0			0
$455$	1.52781	+	1.11002i	0.0716249	+	0.0520385i
$456$		0			0
$457$	10.3366	+	31.8129i	0.483527	+	1.48814i	0.834103	+	0.551608i	$0.185986\pi$
$457$	10.3366	+	31.8129i	0.483527	+	1.48814i	−0.350576	+	0.936534i	$0.614014\pi$
$458$		0			0
$459$	23.2696	−	16.9064i	1.08613	−	0.789122i
$460$		0			0
$461$	12.3468			0.575050			0.287525	−	0.957773i	$-0.407168\pi$
$461$	12.3468			0.575050			0.287525	+	0.957773i	$0.407168\pi$
$462$		0			0
$463$	18.9206			0.879313			0.439656	−	0.898166i	$-0.355100\pi$
$463$	18.9206			0.879313			0.439656	+	0.898166i	$0.355100\pi$
$464$		0			0
$465$	−37.3308	+	27.1224i	−1.73118	+	1.25777i
$466$		0			0
$467$	−1.18490	−	3.64675i	−0.0548307	−	0.168752i	0.919891	−	0.392174i	$-0.128277\pi$
$467$	−1.18490	−	3.64675i	−0.0548307	−	0.168752i	−0.974722	+	0.223423i	$0.928277\pi$
$468$		0			0
$469$	0.856409	+	0.622217i	0.0395453	+	0.0287313i
$470$		0			0
$471$	4.15610	−	12.7912i	0.191503	−	0.589385i
$472$		0			0
$473$	2.11009	−	4.64334i	0.0970222	−	0.213501i
$474$		0			0
$475$	10.5759	−	32.5492i	0.485254	−	1.49346i
$476$		0			0
$477$	−9.88263	−	7.18015i	−0.452494	−	0.328756i
$478$		0			0
$479$	1.05115	+	3.23511i	0.0480284	+	0.147816i	0.972195	−	0.234174i	$-0.0752387\pi$
$479$	1.05115	+	3.23511i	0.0480284	+	0.147816i	−0.924166	+	0.381991i	$0.875239\pi$
$480$		0			0
$481$	0.203532	−	0.147875i	0.00928026	−	0.00674250i
$482$		0			0
$483$	−9.50003			−0.432266
$484$		0			0
$485$	12.1707			0.552644
$486$		0			0
$487$	4.89134	−	3.55377i	0.221648	−	0.161037i	−0.471420	−	0.881909i	$-0.656258\pi$
$487$	4.89134	−	3.55377i	0.221648	−	0.161037i	0.693068	+	0.720872i	$0.256258\pi$
$488$		0			0
$489$	4.71870	+	14.5227i	0.213387	+	0.656738i
$490$		0			0
$491$	−2.90705	−	2.11210i	−0.131193	−	0.0953176i	0.520253	−	0.854012i	$-0.325838\pi$
$491$	−2.90705	−	2.11210i	−0.131193	−	0.0953176i	−0.651447	+	0.758694i	$0.725838\pi$
$492$		0			0
$493$	16.2708	−	50.0762i	0.732798	−	2.25532i
$494$		0			0
$495$	5.72396	−	12.5958i	0.257273	−	0.566138i
$496$		0			0
$497$	−1.77103	+	5.45067i	−0.0794416	+	0.244496i
$498$		0			0
$499$	3.70529	+	2.69205i	0.165872	+	0.120513i	0.667624	−	0.744498i	$-0.267311\pi$
$499$	3.70529	+	2.69205i	0.165872	+	0.120513i	−0.501753	+	0.865011i	$0.667311\pi$
$500$		0			0
$501$	−1.48958	−	4.58447i	−0.0665497	−	0.204819i
$502$		0			0
$503$	18.3533	−	13.3345i	0.818335	−	0.594555i	−0.0979001	−	0.995196i	$-0.531213\pi$
$503$	18.3533	−	13.3345i	0.818335	−	0.594555i	0.916235	+	0.400641i	$0.131213\pi$
$504$		0			0
$505$	1.88963			0.0840874
$506$		0			0
$507$	16.7052			0.741904
$508$		0			0
$509$	−8.52525	+	6.19396i	−0.377875	+	0.274542i	−0.760469	−	0.649374i	$-0.775031\pi$
$509$	−8.52525	+	6.19396i	−0.377875	+	0.274542i	0.382594	+	0.923917i	$0.375031\pi$
$510$		0			0
$511$	−2.39724	−	7.37796i	−0.106048	−	0.326382i
$512$		0			0
$513$	−26.2902	−	19.1009i	−1.16074	−	0.843327i
$514$		0			0
$515$	−3.37694	+	10.3931i	−0.148806	+	0.457977i
$516$		0			0
$517$	−6.62702	−	32.3954i	−0.291456	−	1.42475i
$518$		0			0
$519$	5.06319	−	15.5829i	0.222249	−	0.684013i
$520$		0			0
$521$	−7.76447	−	5.64122i	−0.340168	−	0.247146i	0.404565	−	0.914509i	$-0.367423\pi$
$521$	−7.76447	−	5.64122i	−0.340168	−	0.247146i	−0.744733	+	0.667363i	$0.767423\pi$
$522$		0			0
$523$	3.76242	+	11.5795i	0.164519	+	0.506338i	0.999001	−	0.0446984i	$-0.0142327\pi$
$523$	3.76242	+	11.5795i	0.164519	+	0.506338i	−0.834481	+	0.551036i	$0.814233\pi$
$524$		0			0
$525$	6.31019	−	4.58462i	0.275399	−	0.200089i
$526$		0			0
$527$	−54.2371			−2.36261
$528$		0			0
$529$	28.9432			1.25840
$530$		0			0
$531$	−2.09642	+	1.52314i	−0.0909769	+	0.0660986i
$532$		0			0
$533$	1.48013	+	4.55536i	0.0641113	+	0.197314i
$534$		0			0
$535$	−23.3994	−	17.0007i	−1.01164	−	0.735002i
$536$		0			0
$537$	9.78963	−	30.1294i	0.422454	−	1.30018i
$538$		0			0
$539$	3.29570	+	0.371927i	0.141956	+	0.0160200i
$540$		0			0
$541$	−12.0205	+	36.9953i	−0.516802	+	1.59055i	0.263178	+	0.964747i	$0.415229\pi$
$541$	−12.0205	+	36.9953i	−0.516802	+	1.59055i	−0.779980	+	0.625805i	$0.784771\pi$
$542$		0			0
$543$	−17.7382	−	12.8875i	−0.761217	−	0.553057i
$544$		0			0
$545$	17.2512	+	53.0936i	0.738958	+	2.27428i
$546$		0			0
$547$	6.16788	−	4.48123i	0.263719	−	0.191603i	−0.448066	−	0.894001i	$-0.647887\pi$
$547$	6.16788	−	4.48123i	0.263719	−	0.191603i	0.711785	+	0.702397i	$0.247887\pi$
$548$		0			0
$549$	−11.7491			−0.501438
$550$		0			0
$551$	−59.4881			−2.53428
$552$		0			0
$553$	0.324448	−	0.235725i	0.0137969	−	0.0100241i
$554$		0			0
$555$	−0.592408	−	1.82325i	−0.0251463	−	0.0773925i
$556$		0			0
$557$	9.75113	+	7.08461i	0.413168	+	0.300184i	0.774883	−	0.632104i	$-0.217809\pi$
$557$	9.75113	+	7.08461i	0.413168	+	0.300184i	−0.361715	+	0.932289i	$0.617809\pi$
$558$		0			0
$559$	0.271604	−	0.835911i	0.0114876	−	0.0353553i
$560$		0			0
$561$	−19.4668	+	11.0413i	−0.821891	+	0.466165i
$562$		0			0
$563$	2.91579	−	8.97387i	0.122886	−	0.378204i	−0.870624	−	0.491949i	$-0.836285\pi$
$563$	2.91579	−	8.97387i	0.122886	−	0.378204i	0.993510	+	0.113745i	$0.0362847\pi$
$564$		0			0
$565$	38.4195	+	27.9134i	1.61632	+	1.17433i
$566$		0			0
$567$	−1.11818	−	3.44141i	−0.0469593	−	0.144526i
$568$		0			0
$569$	26.9380	−	19.5716i	1.12930	−	0.820485i	0.143708	−	0.989620i	$-0.454098\pi$
$569$	26.9380	−	19.5716i	1.12930	−	0.820485i	0.985593	+	0.169135i	$0.0540975\pi$
$570$		0			0
$571$	−24.0497			−1.00645			−0.503224	−	0.864156i	$-0.667853\pi$
$571$	−24.0497			−1.00645			−0.503224	+	0.864156i	$0.667853\pi$
$572$		0			0
$573$	−7.24328			−0.302593
$574$		0			0
$575$	−34.5021	+	25.0673i	−1.43884	+	1.04538i
$576$		0			0
$577$	−0.299928	−	0.923082i	−0.0124861	−	0.0384284i	0.944619	−	0.328168i	$-0.106431\pi$
$577$	−0.299928	−	0.923082i	−0.0124861	−	0.0384284i	−0.957105	+	0.289740i	$0.906431\pi$
$578$		0			0
$579$	−8.22289	−	5.97428i	−0.341732	−	0.248283i
$580$		0			0
$581$	1.72117	−	5.29722i	0.0714062	−	0.219766i
$582$		0			0
$583$	23.6827	+	21.6546i	0.980837	+	0.896843i
$584$		0			0
$585$	0.736768	−	2.26754i	0.0304616	−	0.0937512i
$586$		0			0
$587$	33.5808	+	24.3978i	1.38603	+	1.00701i	0.996288	+	0.0860812i	$0.0274345\pi$
$587$	33.5808	+	24.3978i	1.38603	+	1.00701i	0.389738	+	0.920926i	$0.372566\pi$
$588$		0			0
$589$	18.9358	+	58.2784i	0.780236	+	2.40132i
$590$		0			0
$591$	22.0545	−	16.0235i	0.907201	−	0.659120i
$592$		0			0
$593$	−17.6297			−0.723964			−0.361982	−	0.932185i	$-0.617900\pi$
$593$	−17.6297			−0.723964			−0.361982	+	0.932185i	$0.617900\pi$
$594$		0			0
$595$	16.9146			0.693433
$596$		0			0
$597$	−5.59740	+	4.06675i	−0.229086	+	0.166441i
$598$		0			0
$599$	−6.21709	−	19.1342i	−0.254023	−	0.781804i	−0.994021	−	0.109194i	$-0.965173\pi$
$599$	−6.21709	−	19.1342i	−0.254023	−	0.781804i	0.739997	−	0.672610i	$-0.234827\pi$
$600$		0			0
$601$	−17.2686	−	12.5464i	−0.704402	−	0.511778i	0.176961	−	0.984218i	$-0.443373\pi$
$601$	−17.2686	−	12.5464i	−0.704402	−	0.511778i	−0.881363	+	0.472440i	$0.843373\pi$
$602$		0			0
$603$	0.412992	−	1.27106i	0.0168183	−	0.0517615i
$604$		0			0
$605$	−18.6526	+	31.1941i	−0.758336	+	1.26822i
$606$		0			0
$607$	14.5111	−	44.6604i	0.588986	−	1.81271i	0.00634709	−	0.999980i	$-0.497980\pi$
$607$	14.5111	−	44.6604i	0.588986	−	1.81271i	0.582639	−	0.812731i	$-0.302020\pi$
$608$		0			0
$609$	−10.9683	−	7.96892i	−0.444457	−	0.322917i
$610$		0			0
$611$	−1.76086	−	5.41938i	−0.0712369	−	0.219245i
$612$		0			0
$613$	22.5826	−	16.4072i	0.912104	−	0.662682i	−0.0294423	−	0.999566i	$-0.509373\pi$
$613$	22.5826	−	16.4072i	0.912104	−	0.662682i	0.941546	+	0.336884i	$0.109373\pi$
$614$		0			0
$615$	36.4989			1.47178
$616$		0			0
$617$	−13.7407			−0.553179			−0.276590	−	0.960988i	$-0.589204\pi$
$617$	−13.7407			−0.553179			−0.276590	+	0.960988i	$0.589204\pi$
$618$		0			0
$619$	−24.8398	+	18.0472i	−0.998397	+	0.725378i	−0.961744	−	0.273950i	$-0.911670\pi$
$619$	−24.8398	+	18.0472i	−0.998397	+	0.725378i	−0.0366530	+	0.999328i	$0.511670\pi$
$620$		0			0
$621$	12.5133	+	38.5121i	0.502143	+	1.54544i
$622$		0			0
$623$	−1.74477	−	1.26765i	−0.0699028	−	0.0507874i
$624$		0			0
$625$	−6.04809	+	18.6141i	−0.241924	+	0.744564i
$626$		0			0
$627$	18.6605	+	17.0625i	0.745228	+	0.681410i
$628$		0			0
$629$	0.696318	−	2.14305i	0.0277640	−	0.0854489i
$630$		0			0
$631$	−4.24571	−	3.08469i	−0.169019	−	0.122800i	0.500060	−	0.865991i	$-0.333311\pi$
$631$	−4.24571	−	3.08469i	−0.169019	−	0.122800i	−0.669079	+	0.743191i	$0.733311\pi$
$632$		0			0
$633$	9.99477	+	30.7607i	0.397256	+	1.22263i
$634$		0			0
$635$	−8.52166	+	6.19135i	−0.338172	+	0.245696i
$636$		0			0
$637$	0.571550			0.0226456
$638$		0			0
$639$	7.23569			0.286239
$640$		0			0
$641$	−32.5344	+	23.6376i	−1.28503	+	0.933629i	−0.999692	−	0.0247978i	$-0.992106\pi$
$641$	−32.5344	+	23.6376i	−1.28503	+	0.933629i	−0.285338	+	0.958427i	$0.592106\pi$
$642$		0			0
$643$	5.72766	+	17.6279i	0.225877	+	0.695177i	0.998201	+	0.0599492i	$0.0190939\pi$
$643$	5.72766	+	17.6279i	0.225877	+	0.695177i	−0.772325	+	0.635228i	$0.780906\pi$
$644$		0			0
$645$	−5.41845	−	3.93674i	−0.213351	−	0.155009i
$646$		0			0
$647$	−12.8929	+	39.6802i	−0.506871	+	1.55999i	0.290731	+	0.956805i	$0.406102\pi$
$647$	−12.8929	+	39.6802i	−0.506871	+	1.55999i	−0.797602	+	0.603184i	$0.793898\pi$
$648$		0			0
$649$	5.92127	−	3.35846i	0.232430	−	0.131831i
$650$		0			0
$651$	−4.31554	+	13.2819i	−0.169139	+	0.520557i
$652$		0			0
$653$	34.3285	+	24.9411i	1.34338	+	0.976021i	0.999312	+	0.0370757i	$0.0118043\pi$
$653$	34.3285	+	24.9411i	1.34338	+	0.976021i	0.344066	+	0.938946i	$0.388196\pi$
$654$		0			0
$655$	−4.57744	−	14.0879i	−0.178855	−	0.550460i
$656$		0			0
$657$	−7.92362	+	5.75685i	−0.309130	+	0.224596i
$658$		0			0
$659$	15.0993			0.588184			0.294092	−	0.955777i	$-0.404983\pi$
$659$	15.0993			0.588184			0.294092	+	0.955777i	$0.404983\pi$
$660$		0			0
$661$	−8.68285			−0.337724			−0.168862	−	0.985640i	$-0.554009\pi$
$661$	−8.68285			−0.337724			−0.168862	+	0.985640i	$0.554009\pi$
$662$		0			0
$663$	−3.12017	+	2.26693i	−0.121177	+	0.0880404i
$664$		0			0
$665$	−5.90541	−	18.1750i	−0.229002	−	0.704795i
$666$		0			0
$667$	59.9711	+	43.5716i	2.32209	+	1.68710i
$668$		0			0
$669$	−1.69107	+	5.20457i	−0.0653805	+	0.201220i
$670$		0			0
$671$	30.6701	+	3.46118i	1.18401	+	0.133618i
$672$		0			0
$673$	12.4126	−	38.2019i	0.478469	−	1.47258i	−0.362752	−	0.931886i	$-0.618163\pi$
$673$	12.4126	−	38.2019i	0.478469	−	1.47258i	0.841221	−	0.540691i	$-0.181837\pi$
$674$		0			0
$675$	−26.8973	−	19.5420i	−1.03528	−	0.752172i
$676$		0			0
$677$	−3.60891	−	11.1071i	−0.138702	−	0.426879i	0.857446	−	0.514574i	$-0.172050\pi$
$677$	−3.60891	−	11.1071i	−0.138702	−	0.426879i	−0.996147	+	0.0876948i	$0.972050\pi$
$678$		0			0
$679$	2.98000	−	2.16510i	0.114362	−	0.0830888i
$680$		0			0
$681$	4.91543			0.188360
$682$		0			0
$683$	−16.6977			−0.638919			−0.319460	−	0.947600i	$-0.603501\pi$
$683$	−16.6977			−0.638919			−0.319460	+	0.947600i	$0.603501\pi$
$684$		0			0
$685$	−30.5768	+	22.2153i	−1.16828	+	0.848804i
$686$		0			0
$687$	4.56826	+	14.0597i	0.174290	+	0.536410i
$688$		0			0
$689$	4.47394	+	3.25051i	0.170444	+	0.123835i
$690$		0			0
$691$	7.80579	−	24.0238i	0.296946	−	0.913907i	−0.685614	−	0.727965i	$-0.740466\pi$
$691$	7.80579	−	24.0238i	0.296946	−	0.913907i	0.982561	−	0.185942i	$-0.0595336\pi$
$692$		0			0
$693$	−0.839200	−	4.10233i	−0.0318786	−	0.155835i
$694$		0			0
$695$	−7.35643	+	22.6408i	−0.279045	+	0.858813i
$696$		0			0
$697$	34.7076	+	25.2165i	1.31464	+	0.955144i
$698$		0			0
$699$	−0.0668132	−	0.205630i	−0.00252711	−	0.00777764i
$700$		0			0
$701$	10.9556	−	7.95967i	0.413785	−	0.300633i	−0.361347	−	0.932431i	$-0.617683\pi$
$701$	10.9556	−	7.95967i	0.413785	−	0.300633i	0.775133	+	0.631799i	$0.217683\pi$
$702$		0			0
$703$	−2.54583			−0.0960180
$704$		0			0
$705$	−43.4218			−1.63536
$706$		0			0
$707$	0.462675	−	0.336153i	0.0174007	−	0.0126423i
$708$		0			0
$709$	−1.45780	−	4.48664i	−0.0547487	−	0.168499i	0.919943	−	0.392052i	$-0.128235\pi$
$709$	−1.45780	−	4.48664i	−0.0547487	−	0.168499i	−0.974692	+	0.223553i	$0.928235\pi$
$710$		0			0
$711$	−0.409620	−	0.297607i	−0.0153620	−	0.0111611i
$712$		0			0
$713$	23.5960	−	72.6210i	0.883677	−	2.71968i
$714$		0			0
$715$	−2.59128	+	5.70221i	−0.0969084	+	0.213250i
$716$		0			0
$717$	−5.05494	+	15.5575i	−0.188780	+	0.581005i
$718$		0			0
$719$	13.7465	+	9.98744i	0.512659	+	0.372469i	0.813831	−	0.581101i	$-0.197378\pi$
$719$	13.7465	+	9.98744i	0.512659	+	0.372469i	−0.301172	+	0.953570i	$0.597378\pi$
$720$		0			0
$721$	1.02203	+	3.14550i	0.0380625	+	0.117144i
$722$		0			0
$723$	−21.3115	+	15.4837i	−0.792583	+	0.575845i
$724$		0			0
$725$	−60.8617			−2.26035
$726$		0			0
$727$	−36.0496			−1.33701			−0.668503	−	0.743710i	$-0.733065\pi$
$727$	−36.0496			−1.33701			−0.668503	+	0.743710i	$0.733065\pi$
$728$		0			0
$729$	−21.6708	+	15.7448i	−0.802623	+	0.583140i
$730$		0			0
$731$	−2.43269	−	7.48705i	−0.0899763	−	0.276919i
$732$		0			0
$733$	4.31751	+	3.13685i	0.159471	+	0.115862i	0.664659	−	0.747147i	$-0.268577\pi$
$733$	4.31751	+	3.13685i	0.159471	+	0.115862i	−0.505188	+	0.863009i	$0.668577\pi$
$734$		0			0
$735$	1.34586	−	4.14214i	0.0496429	−	0.152785i
$736$		0			0
$737$	−1.45253	+	3.19635i	−0.0535047	+	0.117739i
$738$		0			0
$739$	4.94513	−	15.2195i	0.181910	−	0.559860i	−0.817972	−	0.575258i	$-0.804902\pi$
$739$	4.94513	−	15.2195i	0.181910	−	0.559860i	0.999881	+	0.0153981i	$0.00490157\pi$
$740$		0			0
$741$	3.52519	+	2.56120i	0.129501	+	0.0940880i
$742$		0			0
$743$	3.02055	+	9.29629i	0.110813	+	0.341048i	0.991051	−	0.133485i	$-0.0426169\pi$
$743$	3.02055	+	9.29629i	0.110813	+	0.341048i	−0.880238	+	0.474533i	$0.842617\pi$
$744$		0			0
$745$	3.80991	−	2.76806i	0.139584	−	0.101414i
$746$		0			0
$747$	−7.03198			−0.257287
$748$		0			0
$749$	−8.75365			−0.319851
$750$		0			0
$751$	20.8902	−	15.1776i	0.762293	−	0.553838i	−0.137320	−	0.990527i	$-0.543849\pi$
$751$	20.8902	−	15.1776i	0.762293	−	0.553838i	0.899613	+	0.436689i	$0.143849\pi$
$752$		0			0
$753$	4.66652	+	14.3621i	0.170057	+	0.523383i
$754$		0			0
$755$	2.76761	+	2.01079i	0.100724	+	0.0731800i
$756$		0			0
$757$	−11.2407	+	34.5952i	−0.408549	+	1.25738i	0.509347	+	0.860561i	$0.329887\pi$
$757$	−11.2407	+	34.5952i	−0.408549	+	1.25738i	−0.917895	+	0.396822i	$0.870113\pi$
$758$		0			0
$759$	−6.31472	−	30.8688i	−0.229210	−	1.12046i
$760$		0			0
$761$	13.1199	−	40.3789i	0.475596	−	1.46373i	−0.369557	−	0.929208i	$-0.620491\pi$
$761$	13.1199	−	40.3789i	0.475596	−	1.46373i	0.845153	−	0.534525i	$-0.179509\pi$
$762$		0			0
$763$	13.6690	+	9.93109i	0.494850	+	0.359530i
$764$		0			0
$765$	−6.59905	−	20.3098i	−0.238589	−	0.734302i
$766$		0			0
$767$	0.949067	−	0.689538i	0.0342688	−	0.0248978i
$768$		0			0
$769$	2.69921			0.0973359			0.0486680	−	0.998815i	$-0.484502\pi$
$769$	2.69921			0.0973359			0.0486680	+	0.998815i	$0.484502\pi$
$770$		0			0
$771$	8.53121			0.307244
$772$		0			0
$773$	32.3823	−	23.5271i	1.16471	−	0.846210i	0.174343	−	0.984685i	$-0.444220\pi$
$773$	32.3823	−	23.5271i	1.16471	−	0.846210i	0.990366	+	0.138475i	$0.0442199\pi$
$774$		0			0
$775$	19.3731	+	59.6241i	0.695901	+	2.14176i
$776$		0			0
$777$	−0.469395	−	0.341036i	−0.0168395	−	0.0122346i
$778$		0			0
$779$	14.9780	−	46.0975i	0.536642	−	1.65162i
$780$		0			0
$781$	−18.8883	−	2.13158i	−0.675875	−	0.0762738i
$782$		0			0
$783$	−17.8578	+	54.9608i	−0.638187	+	1.96414i
$784$		0			0
$785$	−27.2746	−	19.8161i	−0.973472	−	0.707268i
$786$		0			0
$787$	−5.73043	−	17.6364i	−0.204268	−	0.628671i	−0.999743	−	0.0226847i	$-0.992779\pi$
$787$	−5.73043	−	17.6364i	−0.204268	−	0.628671i	0.795475	−	0.605986i	$-0.207221\pi$
$788$		0			0
$789$	6.38458	−	4.63867i	0.227297	−	0.165141i
$790$		0			0
$791$	14.3726			0.511032
$792$		0			0
$793$	5.31890			0.188880
$794$		0			0
$795$	34.0922	−	24.7694i	1.20912	−	0.878480i
$796$		0			0
$797$	−4.80110	−	14.7763i	−0.170064	−	0.523402i	0.829310	−	0.558789i	$-0.188734\pi$
$797$	−4.80110	−	14.7763i	−0.170064	−	0.523402i	−0.999374	+	0.0353867i	$0.988734\pi$
$798$		0			0
$799$	−41.2907	−	29.9994i	−1.46076	−	1.06130i
$800$		0			0
$801$	−0.841394	+	2.58955i	−0.0297292	+	0.0914971i
$802$		0			0
$803$	22.3800	−	12.6936i	0.789772	−	0.447948i
$804$		0			0
$805$	−7.35875	+	22.6479i	−0.259362	+	0.798234i
$806$		0			0
$807$	−2.75973	−	2.00506i	−0.0971472	−	0.0705816i
$808$		0			0
$809$	−0.161897	−	0.498267i	−0.00569199	−	0.0175181i	0.948170	−	0.317763i	$-0.102932\pi$
$809$	−0.161897	−	0.498267i	−0.00569199	−	0.0175181i	−0.953862	+	0.300245i	$0.902932\pi$
$810$		0			0
$811$	19.9554	−	14.4985i	0.700729	−	0.509110i	−0.179440	−	0.983769i	$-0.557429\pi$
$811$	19.9554	−	14.4985i	0.700729	−	0.509110i	0.880170	+	0.474659i	$0.157429\pi$
$812$		0			0
$813$	−12.7566			−0.447392
$814$		0			0
$815$	38.2769			1.34078
$816$		0			0
$817$	−7.19560	+	5.22791i	−0.251742	+	0.182901i
$818$		0			0
$819$	−0.222984	−	0.686273i	−0.00779168	−	0.0239803i
$820$		0			0
$821$	−26.0712	−	18.9418i	−0.909890	−	0.661074i	0.0310968	−	0.999516i	$-0.490100\pi$
$821$	−26.0712	−	18.9418i	−0.909890	−	0.661074i	−0.940987	+	0.338442i	$0.890100\pi$
$822$		0			0
$823$	−5.94728	+	18.3039i	−0.207309	+	0.638032i	0.792301	+	0.610130i	$0.208883\pi$
$823$	−5.94728	+	18.3039i	−0.207309	+	0.638032i	−0.999611	+	0.0279024i	$0.991117\pi$
$824$		0			0
$825$	19.0914	+	17.4565i	0.664676	+	0.607757i
$826$		0			0
$827$	15.4791	−	47.6397i	0.538261	−	1.65660i	−0.198235	−	0.980154i	$-0.563521\pi$
$827$	15.4791	−	47.6397i	0.538261	−	1.65660i	0.736496	−	0.676442i	$-0.236479\pi$
$828$		0			0
$829$	4.26306	+	3.09729i	0.148062	+	0.107573i	0.659350	−	0.751836i	$-0.270831\pi$
$829$	4.26306	+	3.09729i	0.148062	+	0.107573i	−0.511288	+	0.859409i	$0.670831\pi$
$830$		0			0
$831$	12.0546	+	37.1004i	0.418171	+	1.28700i
$832$		0			0
$833$	4.14155	−	3.00901i	0.143496	−	0.104256i
$834$		0			0
$835$	−12.0831			−0.418154
$836$		0			0
$837$	59.5276			2.05757
$838$		0			0
$839$	−15.8160	+	11.4910i	−0.546030	+	0.396714i	−0.826319	−	0.563202i	$-0.809569\pi$
$839$	−15.8160	+	11.4910i	−0.546030	+	0.396714i	0.280290	+	0.959915i	$0.409569\pi$
$840$		0			0
$841$	23.7291	+	73.0307i	0.818245	+	2.51830i
$842$		0			0
$843$	−17.3597	−	12.6125i	−0.597898	−	0.434399i
$844$		0			0
$845$	12.9399	−	39.8249i	0.445146	−	1.37002i
$846$		0			0
$847$	0.982158	+	10.9561i	0.0337474	+	0.376455i
$848$		0			0
$849$	−4.65755	+	14.3345i	−0.159847	+	0.491958i
$850$		0			0
$851$	2.56651	+	1.86468i	0.0879787	+	0.0639203i
$852$		0			0
$853$	−3.30892	−	10.1838i	−0.113295	−	0.348687i	0.878292	−	0.478124i	$-0.158683\pi$
$853$	−3.30892	−	10.1838i	−0.113295	−	0.348687i	−0.991588	+	0.129437i	$0.958683\pi$
$854$		0			0
$855$	−19.5192	+	14.1815i	−0.667541	+	0.484997i
$856$		0			0
$857$	−22.8046			−0.778992			−0.389496	−	0.921028i	$-0.627351\pi$
$857$	−22.8046			−0.778992			−0.389496	+	0.921028i	$0.627351\pi$
$858$		0			0
$859$	−21.5072			−0.733815			−0.366907	−	0.930258i	$-0.619583\pi$
$859$	−21.5072			−0.733815			−0.366907	+	0.930258i	$0.619583\pi$
$860$		0			0
$861$	8.93676	−	6.49293i	0.304564	−	0.221279i
$862$		0			0
$863$	−9.03202	−	27.7977i	−0.307454	−	0.946245i	−0.978750	−	0.205056i	$-0.934262\pi$
$863$	−9.03202	−	27.7977i	−0.307454	−	0.946245i	0.671297	−	0.741189i	$-0.265738\pi$
$864$		0			0
$865$	−33.2274	−	24.1411i	−1.12977	−	0.820823i
$866$		0			0
$867$	−3.75008	+	11.5416i	−0.127359	+	0.391972i
$868$		0			0
$869$	0.981613	+	0.897552i	0.0332989	+	0.0304474i
$870$		0			0
$871$	−0.186965	+	0.575419i	−0.00633507	+	0.0194973i
$872$		0			0
$873$	−3.76229	−	2.73346i	−0.127334	−	0.0925137i
$874$		0			0
$875$	−0.936600	−	2.88256i	−0.0316629	−	0.0974482i
$876$		0			0
$877$	42.8215	−	31.1116i	1.44598	−	1.05056i	0.459228	−	0.888318i	$-0.348126\pi$
$877$	42.8215	−	31.1116i	1.44598	−	1.05056i	0.986750	−	0.162246i	$-0.0518739\pi$
$878$		0			0
$879$	−18.1952			−0.613709
$880$		0			0
$881$	−4.46364			−0.150384			−0.0751919	−	0.997169i	$-0.523957\pi$
$881$	−4.46364			−0.150384			−0.0751919	+	0.997169i	$0.523957\pi$
$882$		0			0
$883$	6.01279	−	4.36855i	0.202346	−	0.147013i	−0.481998	−	0.876172i	$-0.660089\pi$
$883$	6.01279	−	4.36855i	0.202346	−	0.147013i	0.684344	+	0.729159i	$0.260089\pi$
$884$		0			0
$885$	−2.76239	−	8.50177i	−0.0928568	−	0.285784i
$886$		0			0
$887$	−6.62993	−	4.81693i	−0.222611	−	0.161737i	0.470890	−	0.882192i	$-0.343933\pi$
$887$	−6.62993	−	4.81693i	−0.222611	−	0.161737i	−0.693501	+	0.720455i	$0.743933\pi$
$888$		0			0
$889$	−0.985124	+	3.03190i	−0.0330400	+	0.101687i
$890$		0			0
$891$	10.4390	−	5.92088i	0.349721	−	0.198357i
$892$		0			0
$893$	−17.8189	+	54.8410i	−0.596287	+	1.83518i
$894$		0			0
$895$	−64.2449	−	46.6767i	−2.14747	−	1.56023i
$896$		0			0
$897$	−1.67788	−	5.16399i	−0.0560229	−	0.172421i
$898$		0			0
$899$	88.1596	−	64.0517i	2.94029	−	2.13624i
$900$		0			0
$901$	49.5317			1.65014
$902$		0			0
$903$	−2.02703			−0.0674553
$904$		0			0
$905$	−44.4637	+	32.3048i	−1.47802	+	1.07385i
$906$		0			0
$907$	−10.8426	−	33.3701i	−0.360023	−	1.10804i	−0.953039	−	0.302846i	$-0.902063\pi$
$907$	−10.8426	−	33.3701i	−0.360023	−	1.10804i	0.593016	−	0.805190i	$-0.297937\pi$
$908$		0			0
$909$	−0.584134	−	0.424398i	−0.0193745	−	0.0140764i
$910$		0			0
$911$	2.82716	−	8.70110i	0.0936680	−	0.288280i	−0.893236	−	0.449588i	$-0.851571\pi$
$911$	2.82716	−	8.70110i	0.0936680	−	0.288280i	0.986904	+	0.161307i	$0.0515710\pi$
$912$		0			0
$913$	18.3565	+	2.07157i	0.607512	+	0.0685589i
$914$		0			0
$915$	12.5247	−	38.5471i	0.414054	−	1.27433i
$916$		0			0
$917$	−3.62694	−	2.63512i	−0.119772	−	0.0870194i
$918$		0			0
$919$	−17.8379	−	54.8994i	−0.588418	−	1.81097i	−0.585086	−	0.810971i	$-0.698939\pi$
$919$	−17.8379	−	54.8994i	−0.588418	−	1.81097i	−0.00333197	−	0.999994i	$-0.501061\pi$
$920$		0			0
$921$	−0.630931	+	0.458398i	−0.0207899	+	0.0151047i
$922$		0			0
$923$	−3.27565			−0.107819
$924$		0			0
$925$	−2.60462			−0.0856394
$926$		0			0
$927$	3.37813	−	2.45436i	0.110952	−	0.0806117i
$928$		0			0
$929$	13.1285	+	40.4053i	0.430732	+	1.32566i	0.897398	+	0.441223i	$0.145455\pi$
$929$	13.1285	+	40.4053i	0.430732	+	1.32566i	−0.466666	+	0.884434i	$0.654545\pi$
$930$		0			0
$931$	−4.67915	−	3.39960i	−0.153353	−	0.111418i
$932$		0			0
$933$	4.43091	−	13.6369i	0.145061	−	0.446453i
$934$		0			0
$935$	11.2433	+	54.9613i	0.367694	+	1.79743i
$936$		0			0
$937$	4.08158	−	12.5618i	0.133339	−	0.410376i	−0.861989	−	0.506928i	$-0.830781\pi$
$937$	4.08158	−	12.5618i	0.133339	−	0.410376i	0.995328	+	0.0965512i	$0.0307812\pi$
$938$		0			0
$939$	32.9406	+	23.9327i	1.07497	+	0.781015i
$940$		0			0
$941$	9.57317	+	29.4632i	0.312076	+	0.960472i	0.976941	+	0.213508i	$0.0684891\pi$
$941$	9.57317	+	29.4632i	0.312076	+	0.960472i	−0.664865	+	0.746964i	$0.731511\pi$
$942$		0			0
$943$	−48.8634	+	35.5013i	−1.59121	+	1.15608i
$944$		0			0
$945$	−18.5645			−0.603905
$946$		0			0
$947$	−34.0069			−1.10508			−0.552539	−	0.833487i	$-0.686341\pi$
$947$	−34.0069			−1.10508			−0.552539	+	0.833487i	$0.686341\pi$
$948$		0			0
$949$	3.58709	−	2.60617i	0.116442	−	0.0845999i
$950$		0			0
$951$	5.85889	+	18.0318i	0.189987	+	0.584721i
$952$		0			0
$953$	−20.6137	−	14.9767i	−0.667744	−	0.485144i	0.201525	−	0.979483i	$-0.435410\pi$
$953$	−20.6137	−	14.9767i	−0.667744	−	0.485144i	−0.869269	+	0.494339i	$0.835410\pi$
$954$		0			0
$955$	−5.61067	+	17.2679i	−0.181557	+	0.558775i
$956$		0			0
$957$	18.6030	−	40.9366i	0.601350	−	1.32329i
$958$		0			0
$959$	−3.53475	+	10.8788i	−0.114143	+	0.351296i
$960$		0			0
$961$	−65.7320	−	47.7571i	−2.12039	−	1.54055i
$962$		0			0
$963$	3.41513	+	10.5107i	0.110051	+	0.338703i
$964$		0			0
$965$	−20.6121	+	14.9755i	−0.663526	+	0.482080i
$966$		0			0
$967$	32.9459			1.05947			0.529735	−	0.848163i	$-0.322291\pi$
$967$	32.9459			1.05947			0.529735	+	0.848163i	$0.322291\pi$
$968$		0			0
$969$	39.0279			1.25376
$970$		0			0
$971$	−28.1280	+	20.4362i	−0.902671	+	0.655829i	−0.939151	−	0.343506i	$-0.888386\pi$
$971$	−28.1280	+	20.4362i	−0.902671	+	0.655829i	0.0364797	+	0.999334i	$0.488386\pi$
$972$		0			0
$973$	2.22643	+	6.85225i	0.0713761	+	0.219673i
$974$		0			0
$975$	3.60659	+	2.62034i	0.115503	+	0.0839181i
$976$		0			0
$977$	−6.18692	+	19.0414i	−0.197937	+	0.609188i	0.801993	+	0.597334i	$0.203773\pi$
$977$	−6.18692	+	19.0414i	−0.197937	+	0.609188i	−0.999930	+	0.0118538i	$0.996227\pi$
$978$		0			0
$979$	2.95926	−	6.51196i	0.0945784	−	0.208123i
$980$		0			0
$981$	6.59169	−	20.2871i	0.210456	−	0.647718i
$982$		0			0
$983$	−10.2104	−	7.41826i	−0.325660	−	0.236606i	0.412927	−	0.910764i	$-0.364506\pi$
$983$	−10.2104	−	7.41826i	−0.325660	−	0.236606i	−0.738587	+	0.674158i	$0.764506\pi$
$984$		0			0
$985$	−21.1164	−	64.9895i	−0.672823	−	2.07074i
$986$		0			0
$987$	−10.6318	+	7.72447i	−0.338414	+	0.245872i
$988$		0			0
$989$	11.0832			0.352424
$990$		0			0
$991$	9.12123			0.289745			0.144873	−	0.989450i	$-0.453723\pi$
$991$	9.12123			0.289745			0.144873	+	0.989450i	$0.453723\pi$
$992$		0			0
$993$	9.48427	−	6.89073i	0.300974	−	0.218671i
$994$		0			0
$995$	5.35930	+	16.4942i	0.169901	+	0.522903i
$996$		0			0
$997$	−40.9753	−	29.7703i	−1.29770	−	0.942835i	−0.297771	−	0.954637i	$-0.596243\pi$
$997$	−40.9753	−	29.7703i	−1.29770	−	0.942835i	−0.999930	+	0.0118023i	$0.996243\pi$
$998$		0			0
$999$	−0.764239	+	2.35209i	−0.0241795	+	0.0744167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.c.141.2	✓	12
11.4	even	5		3388.2.a.u.1.3		6
11.5	even	5	inner	308.2.j.c.225.2	yes	12
11.7	odd	10		3388.2.a.t.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.c.141.2	✓	12	1.1	even	1	trivial
308.2.j.c.225.2	yes	12	11.5	even	5	inner
3388.2.a.t.1.3		6	11.7	odd	10
3388.2.a.u.1.3		6	11.4	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06640 - 0.774782i) q^{3} +(-1.02103 - 3.14242i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.390138 + 1.20072i) q^{9} +O(q^{10})\)	\(q+(1.06640 - 0.774782i) q^{3} +(-1.02103 - 3.14242i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.390138 + 1.20072i) q^{9} +(1.37215 - 3.01947i) q^{11} +(0.176619 - 0.543577i) q^{13} +(-3.52351 - 2.55998i) q^{15} +(-1.58193 - 4.86868i) q^{17} +(-4.67915 + 3.39960i) q^{19} -1.31814 q^{21} +7.20716 q^{23} +(-4.78720 + 3.47810i) q^{25} +(1.73624 + 5.34359i) q^{27} +(8.32105 + 6.04559i) q^{29} +(3.27397 - 10.0762i) q^{31} +(-0.876173 - 4.28307i) q^{33} +(-1.02103 + 3.14242i) q^{35} +(0.356105 + 0.258725i) q^{37} +(-0.232808 - 0.716509i) q^{39} +(-6.77984 + 4.92584i) q^{41} +1.53780 q^{43} +4.17152 q^{45} +(8.06579 - 5.86014i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-5.45913 - 3.96629i) q^{51} +(-2.98993 + 9.20205i) q^{53} +(-10.8895 - 1.22890i) q^{55} +(-2.35588 + 7.25065i) q^{57} +(1.66051 + 1.20643i) q^{59} +(2.87574 + 8.85062i) q^{61} +(1.02140 - 0.742087i) q^{63} -1.88848 q^{65} -1.05858 q^{67} +(7.68568 - 5.58398i) q^{69} +(-1.77103 - 5.45067i) q^{71} +(6.27607 + 4.55983i) q^{73} +(-2.41028 + 7.41807i) q^{75} +(-2.88489 + 1.63627i) q^{77} +(-0.123928 + 0.381412i) q^{79} +(2.92744 + 2.12691i) q^{81} +(1.72117 + 5.29722i) q^{83} +(-13.6842 + 9.94218i) q^{85} +13.5575 q^{87} +2.15666 q^{89} +(-0.462394 + 0.335949i) q^{91} +(-4.31554 - 13.2819i) q^{93} +(15.4606 + 11.2328i) q^{95} +(-1.13826 + 3.50320i) q^{97} +(3.09022 + 2.82558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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